scholarly journals The dynamics and geometry of free group endomorphisms

2021 ◽  
Vol 384 ◽  
pp. 107714
Author(s):  
Jean Pierre Mutanguha
Keyword(s):  
Author(s):  
Michele Rossi ◽  
Lea Terracini

AbstractLet X be a $$\mathbb {Q}$$ Q -factorial complete toric variety over an algebraic closed field of characteristic 0. There is a canonical injection of the Picard group $$\mathrm{Pic}(X)$$ Pic ( X ) in the group $$\mathrm{Cl}(X)$$ Cl ( X ) of classes of Weil divisors. These two groups are finitely generated abelian groups; while the first one is a free group, the second one may have torsion. We investigate algebraic and geometrical conditions under which the image of $$\mathrm{Pic}(X)$$ Pic ( X ) in $$\mathrm{Cl}(X)$$ Cl ( X ) is contained in a free part of the latter group.


2021 ◽  
Vol 116 (4) ◽  
pp. 369-383
Author(s):  
Stefano Francaviglia ◽  
Armando Martino ◽  
Dionysios Syrigos

AbstractWe study the minimally displaced set of irreducible automorphisms of a free group. Our main result is the co-compactness of the minimally displaced set of an irreducible automorphism with exponential growth $$\phi $$ ϕ , under the action of the centraliser $$C(\phi )$$ C ( ϕ ) . As a corollary, we get that the same holds for the action of $$ <\phi>$$ < ϕ > on $$Min(\phi )$$ M i n ( ϕ ) . Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.


1983 ◽  
Vol 11 (22) ◽  
pp. 2519-2525 ◽  
Author(s):  
Chander Kanta Gupta
Keyword(s):  

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Enrique Miguel Barquinero ◽  
Lorenzo Ruffoni ◽  
Kaidi Ye

Abstract We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank. In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.


2021 ◽  
Vol 252 (6) ◽  
pp. 782-783
Author(s):  
A. I. Generalov ◽  
A. S. Mironov
Keyword(s):  

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Dai Woo Kim ◽  
Jonghoon Shin ◽  
Chang Kyu Lee ◽  
Myungjin Kim ◽  
Sohyeon Lee ◽  
...  

AbstractGiven that nonadherence is related to subject characteristics and drug tolerance and preserved eye drops tend to be more intolerable than preservative-free ones, we conducted a phase 4, parallel-grouped, investigator-blind, active-control, randomized, multicenter study. A total of 51 patients with intraocular pressure (IOP) ≥ 15 mmHg diagnosed with open-angle glaucoma or ocular hypertension were randomly assigned to the preserved latanoprost group (n = 26) and the preservative-free latanoprost group (n = 25). The efficacy variables were corneal/conjunctival staining grade, Ocular Surface Disease Index (OSDI), adherence at 12 weeks after the first administration; corneal/conjunctival staining grade at 4 weeks; and IOP, tear break-up time (TBUT), and hyperemia score at 4 and 12 weeks. The safety variables included visual acuity and drug tolerance questionnaire results. There was no statistically significant difference in corneal/conjunctival staining grade, OSDI, or TBUT between the groups at 4 and 12 weeks. However, the adherence rate was higher and the hyperemia score was lower in the preservative-free group than in the preserved group. The severity and duration of stinging/burning sensation were lower in the preservative-free group than in the preserved group. Overall, preservative-free latanoprost showed better ocular tolerance assessed by hyperemia scores and stinging/burning symptoms following higher adherence than preserved latanoprost.


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